The present invention relates generally to communication systems (for example, wireless communication systems) and, in particular, to a method and apparatus for higher dimensional modulation to provide more effective communications.
Space-time coding (STC) is well known in the art. In an STC encoder, binary valued symbols (i.e., binary valued symbols bi xcex5[0,1]) are encoded such that code words are drawn from an M-ary alphabet (i.e., si xcex5[c0, c1, . . . cMxe2x88x921]) and transmitted on multiple antennas. Assuming that the channels between each transmit antenna and receiver experiences independent flat fading, the spatial diversity provided by the multiple antenna improves the likelihood of correctly receiving the transmitted data using diversity reception techniques. An exemplary STC [coder] system 100 is illustrated in FIG. 1.
A binary valued data source 102 is channel coded 104 and/or interleaved based upon the performance requirements of the communication system under consideration. Channel coding and interleaving provides a measure of protection against corruption of the data during transmission over an imperfect channel. The output of conventional channel coding is then passed to the STC encoder 106. The example shown in FIG. 1 comprises two constitutive convolutional encoders, although other types of encoders may be used. As known in the art, the STC encoder 106 introduces structured memory to the data thereby improving its robustness to induced errors. The binary valued outputs 114, 116 are passed to a symbol encoder 108 that produces M-ary symbols for each of the two transmit antennas 110, 112. That is, groups of log2(M) of the binary outputs 114, 116 are mapped into ones if M possible symbols. One important characteristic of the prior art STC [coder] system 100 is that the codewords [c0, . . . cMxe2x88x922, cMxe2x88x921] representing the M possible symbols are defined relative to a two-dimensional basis vector, (I,Q). This is illustrated in FIG. 2 where the points in the signal constellation 200 are for 16-QAM, and each point cj for j=0 to Mxe2x88x921 corresponds to a four-bit word.
Because the distance between codewords governs error rate performance, in part, it is desirable to maximize the distance between codewords. One important metric used in quantifying performance in wireless communications systems is the minimum distance between codewords, dmin. It has been shown that the error rate for data transmitted in this manner is proportional to dmin. One way to increase dmin is to increase the number of dimensions over which the M possible symbols are defined. For example, assuming a signal constellation in which M=4 defined on a unit circle within a two-dimensional (I, Q) plane, it can be shown that the minimum squared distance between the symbols is 2. However, by defining the same four symbols on a unit sphere within a three-dimensional space, the minimum squared distance can be increased to 2.66, thereby resulting in a 1.23 decibel (dB) improvement in performance.
Although the concept of higher dimensional modulation schemes (e.g., lattice codes and spherical codes) have been around for quite some time, their application has been limited to analyzing the performances of channel coding schemes. Designers have been hesitant to directly implement these higher dimensional modulation schemes for fear that they would require a radical change in conventional modulation and demodulation design. Other authors have attempted to use codes constructed using cosets and lattices built up using multiple transmissions of two-dimensional constellations such as multiple phase shift keying (MPSK) and multiple quadrature amplitude modulation (MQAM). Lattice codes constructed in such a fashion have been termed product codes as they are constructed by a Cartesian product of L two-dimensional signals. The popularity of these multidimensional codes can be attributed to their inherent capability to perform set partitioning and branch labeling in multidimensions by performing each in two dimensions for all constituent pairs of coordinates. One drawback of these codes, which is common to all MQAM signaling schemes, is the very large peak to average power ratio (PAPR) for the transmitted symbols. A large PAPR requires the input signal power to the transmit amplifier to be backed off from its saturation level and, thus, resulting in poor DC power efficiency for the transmitter. For two-dimensional signals, M-PSK signals are used to lower the PAPR. The multidimensional analogy is to use signal points that lie on an N-dimensional sphere. Another disadvantage of product codes is that they do not always achieve (or approach) the Levinstein""s bound in minimum squared distance. The main reason is that the symbols are forced to fall off a lattice structure that may not be optimum depending on the constellation size M and number of dimensions N. Furthermore, since the codes are built up from smaller two-dimensional signals, there are only a finite number of allowable coordinates in each dimension.
Thus, a need exists for techniques whereby higher dimensional modulation is achieved in any number of allowable coordinate sets and dimensions greater than two to improve system performance.
The present invention provides a method and apparatus for providing N-dimensional modulation, where N is greater than two. This is achieved by first defining an M-ary signal constellation within an N-dimensional space. In a preferred embodiment, each of the M symbols from this constellation are defined such that they each reside upon the surface of an N-dimensional sphere and such that the minimum distance between symbols is maximized. N orthogonal functions are then used as the bases for representing the N-dimensional symbols for transmission. For example, the orthogonal subcarriers within an orthogonal frequency division multiplexing system may be used for this purpose. Further examples of orthogonal functions possessing orthogonality in time and space are also described for this purpose. In one embodiment of the present invention, conventional quadrature amplitude modulation symbol encoding may be used to represent the N-dimensional symbols, thereby facilitating the use of conventional modulation techniques. Using these techniques, the present invention is capable of improving the overall performance of space-time coding systems.